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I lived in Taipei for a couple of years. The "third space" is super common there. People would hang out at coffee shops (loads and loads of coffee shops), get "afternoon tea" with friends, or go to a park or even a subway station lobby and socialize.
The Taipei metro even embraced it and set up specific places / spaces for shopping or socializing (that were dual purpose rather than simply being a corridor).
I feel like this is missing in the US, and genuinely miss wandering around with my backpack for a Saturday. It was a load of fun to head out for an early lunch, go find some random coffee shop to "work" (aka "surf the web and people watch"), then find a place for a beverage and maybe go see a movie or have dinner. Those days were genuinely the most fulfilling, especially when I'd run into random acquaintances.
Bringing it back, a river runs through downtown Austin with a great hike / bike trial along it. There aren't really many cafes (I can think of one) along about 10 miles of trail that are good "destinations" to wander toward while enjoying the scenery.
May be a bit early yet for this though. Would tend to displace other "hang-out" locations and businesses, so might be best to fit in with what's there (bars?), but offer something new and different (so people have an idea to anchor on rather than going entirely new concept).
Bakeries also fit this description in those neighborhoods.
I believe it's owned by a local bank, but I don't know if it makes money (or if it's intended to). Entry is free normally, sometimes there are non-free ticketed concerts and a cash bar.
I'd love to have an accessible chill out place I could go to just to get some work done, preferably with a good view of something. No music playing, just quiet and the ability to get a coffee and simple food if necessary.
Google Campus in London does this, but isn't that comfortable for long periods (plus it's absolutely packed).